The application of digital and analog computers to thermal analysis

Thermochimica Acra, 5 (1973) 225-242 @J EIsevier Scientific Publishing Company,

Amsterdam -

225

Printed in Belgium

Review

THE APPLICATION OF THERMAL ANALYSIS W.

W.

DIGITAL

AND

ANALOG

COMPUTERS

TO

WENDLANDT

Department of Chemistry, Unicrersityof Houston. Houston, Texas 77004 (U_ S. A.) (Received

6 June 1972)

AB!TiTRACT

The apphcations of digital and analog computers to problems in thermal analysis are reviewed. AI1 of the applications are of a passire type in which there is no significant computer control of the experiment. Techniques discussed include thermogravimetry (TG), differential thermal analysis (DTA), differential scanning caIorimetry (DSC), gas evolution analysis (GEA), 2nd mass spectrometric thermal analysis (MTA). I?Ti-RODUCl-IOS

Ahhough there are numerous applications of digita and analog computers to most chemical laboratory techniques’ 3, there have been relatively few applications to thermal analysis. All of the applications that have been described are of a parsire type in which there is no significant computer control of the experiment. There have been no applications of the actice type in which the computer is involved to some extent in the control of the instrument. This review attempts to summarize the important applications of computers to thermal analysis techniques. Because of the dif3cuity in searching the literature for this type of information, no attempt has been made to write a comprehensive treatment of the subject. Rather, it is hoped that this review wiIl include the more important investigations. For convenience, the discussion is divided into applications in thermogravimetry (TG), differential thermaI anaIysis (DTA) and differential scanning calorimetry

@SC),

THERMOORAVIMEIRY

and miscellaneous

techniques.

(TG)

One of the first applications of a digitai computer to calculations of thermogravimetric data was that by SouIen ‘. Since the amount of computation required to obtain kinetics constants from TG is large, a computer program was developed for the calculation of temperature, weight, and rate of reaction from the d-c. voltage

generated by the thermobalance. A Remington Rand Univac computer was used, employing a Math-_Matic compiling system, in which a 23-sentence English language pro,m.rn was used to compute 60 va!ues each of temperature, weight, cumulative weight-Ioss, and the rate of reaction, and to store these for subsequent computation of the kinetics constants_ Instead of a data logging system, numerical va!ues were manually taken from the strip-chart recordings at one minute intervak and used as inplut into the computer. It was stated that an EngIish language program was rather inefficient for this type of program and that a more efficient program could no doubt be developed usin,D machine languageAlmost al! of the other applications of computers to thermogravimetry invoived calculations pertaining to reaction kinetics_ Schempf ef al.* developed a program, POLY 2, for the determination of the pre-exponentia! factor of the Arrhenius equation and the activation energy. This pro-mm, designed to accept sample weight, LC,and sample temperature, T, values as a function of time, t, was written for firstord!er reactions oniy, although with slight modifications it could be used for any order of reaction _ It made use of a Ieast squares polynomial fit of the time-sample weight values to the equation w =

c

c(i+l)t(i)

(1)

i=O

where n is the desired order polynomial, C the coefficient of the polynomial and t the time_ From the x-1 curve thereby generated, an additional Fortran subroutine, FREEB, calcu!ated the reaction rate constant for any point on the TG curve using the equation

(2)

where n is the desired order poIynomia!_ A Ieast squares ana!ysis of the va!ues of log k versus 1000/T was obtained for t!x following tit-order polynomial Iog k = !og A - E@2_303 R (Noojr).

(3)

The complete program is illustrated by the fiow diagram in Fig_ 1. The accuracy of the computer fit of the TG curve was 0.2 mg whi!e the limit of accuracy for reading a weight va!ue was 0. ! mg. Two pro_erzlms for the algorithmization of kinetic data computations from TG curies were developed by Sestak ez rr1.3.They made use of the basic equation &jQiz=exp

(--E,‘RT)(I

-I)’

(4)

where Q is the degree of decomposition and n the order of reaction. The kinetics parameters, E, 2, and n, were evaluated by use of two differential methods. The first

227

POLY 2

Read : Polynomial

order

-m-----m-_

Subroutine

+:-------

FREE6

Read : Time-temperature

data

Points sample weight at time equal to infinity

Calculate:

Weight

and

slope at chosen

time

I Ca!culate: weight remaining,convert temperature to OK determine reactions rate constant

Test for positive weight remaining and correct slope and reject bad data

points

I

Convert data to reaction rate log va iues and 10031 r for analysis I

exponential

factor

by least

squares

1 End of program

analysis

1

Fig- 1. FIow dia_g-am for calcuIation2_

method utilized a least squares polynomial fit of the TG curve with a j-th order polynomial

a=A,+A,x+...Aixi

(5)

wherej is about 13 and A's are constants obtained from the least squares fit of the

228 experimental data. The second method attempted to use the simpkst means of obtaining a derivative of the obsenxd TG curve by numerical derivation using the first three terms of the series (dz;dr),=

((K;,J-r+,)/2-

.-. i

i(icjt~-4r~~izf5zrj,,--5rri_,i4rci-z-~i_~)l160-

. . . + . ..)/Qzo.,

(6)

u-here x is the weight Ioss and Q is a constant time interval of scanning. This program was written in ALGOL 60_ The results obtained by computing data obtained from TG curves, with various pro-grams and with those caIculated manually, are shown in Table 1. The discrepancies which occur were said to be due to differences in the requirements for the input data. A flow-chart for the second program used was also presented in detai1. TzXBLE I COhfPARISOS Everimemal

BmWEES &-la used

C~c~O~-+CSc93 from rcf 4

+

co

1fXNUAL

XXD

COT%fPLTER

CALCULATIONS3

Mcmuai resdls

Compiler

DerirGrire*

Integr&

Freq. fucro#

Propam

E=

73.1 *3s 1

74 I

72.1 1

I

Program

2

&)

E==7i=:kcd.n=0_7

67% IS

n =0_6

58.67 O-591

Gallagher and his co-workers have described several TG data collection systems in which the data are obtained on magnetic tape or on punched paper tape. A block diagram of their first system’ is shown in Fig. 2. In this system, the outputs from the Cahn Model RG balance and the Chro,nel-Alumel thermocouple were conberted to digital form and punched on paper tape for subsequent computer processing- The timing cycle for the counter was normally set to count the thermocoupIe channel for one szc and the weight channel for 99 sec. Switching time was relatil-ely instantaneous and the data were punched whiIe the counter is operating so that the dead time was neggigible_ The effective use of averaging each reading over these times leads to a reduction of noise which is important for the computation of the time derivative_ The digitai data were transferred from punched paper tape to cards and the EMF versus temperature tables for the compensated thermocouple were fit by a least squares technique to the equation “C= 22.2877+2X7003

(mV)-0.1050

(mV)*+O_OOI7 (m\y3

(7)

which was satisfactory to i I “C over the temperature region of 200” to 1000°C. A pro_eram was developec! to compute the average temperature for each pair of consecutive temperature readings and associate this temperature with the average weight

229

COUNTER

INTERFACE I PAPER PUNCH

1

Fig. 2. Block diagram of digital TG system of Gal!agher and Schrey’.

readings in the interval between the thermocouple readings. A General Efectric Model 600 computer then tabuiated and plotted both the percent weight-loss and the rate of weight-loss (mg/min) as a function of temperature. The rate of weigh&-Iosswas obtained from the difference in weight of consecutive readings (100 set intervals) and corrected to give mgimin. No further refinement or smoothing of the differential da@ was necessary. For isothermal measurements, using a Cahn Model RG thermobalance, the data acquisition system shown in Fig. 3 was employed I I* ’ ‘. The system accepted up to four analog input signals in which two were used for weight and temperature, respectiveIy. The voltages were converted to frequency using a voItage-to-frequency converter and four channek were simultaneously counted on four scalers for a predetermined time interval. The magnetic tape interface served as the control center. In the automatic mode, the data were scanned repeatedIy at a preset time interval and placed on the magnetic tape along with channel identification numbers. A fifth channel couId be created to insert a six digit number for labeling or control purposes. Data processing consisted of transferring the data from tape onto the disc storage of a Honeywell Model 635 Computer in appropriate arrays corresponding to each channel. Computer generated plots of each array as a function of time were then made with subsequent data processing as previously described’ 2.

2310

OPTION

COUPLE

VOLTAGE

I

r

TH ERMO-

BALANCE

TO

OPTION

+

4

FREQUENCY

CONVERTERS

c

v

* SCALERS , t TIMERS

__

r

INTERFACE

*

PARAMETRIC DATA

!

MAGNETIC

FG. 3. Data acqukition system of GaIIaghcr and Johnscn”-

=2_

Gallagher and co-worker?’ ‘- ’ 3 also described a modification of the PerkinElmer thermobalance to obtain the data in digital form. In this instrument, the platinum furnace heater winding serves also as the temperature sensor. It forms one side of a bridge circuit while the other side is driven by the output voltage from the programming potentiometer. T&s same voltage is used to supply the temperature 2 w2 i

/ 10.1

03

PER

CENT

100

rv,

\ iQ2

/ 202

WEIGHT

“C To *

%I 100

303

30.4

UfJ

?OO b-2 wo 4. Thing

5

404

MglMIN TI

* T2 2

T2 + T3

405

SEC

“C

SOCv+,-w,

2

wo

Fis

\ 203

1

TI

-‘N21

T2

10.1 SOW+

10.1 6Ot Wp -W3 1

2 sequcna employed by digital thcrmobdana*.

7 01

T3

231

portion of the digital equipment and is directly related to temperature by use of magnetic (Curie point) TG cahbration standards. The two input voltages were converted to frequency and counted for a predetermined time in the sequence as shown in Fig. 4. The temperature signal was counted for 0.1 set and then automatically switched to the weight signal for 10 sec. The output data were constantly punched on paper tape for input into the computer. The first stage in the computer processing of the punched tape data was to transfer the data to cards and to use these cards for the three steps in processing’. The first step was to obtain a graphical output of the weight as a function of time, as shown in Fig. 5. The second step of data handling consisted of utiiizing the initial and MG.

f

Mn(N0$2-12f-l20

Mn203

TIME Fig. 5. Weight versus time curves as reported by Gallagher and Johnsong.

6na.l weights for each interval to determine values of z, the fraction reacted. The computer, having calculated the values of a for each point then plotted these to conform to the eighteen equations given in Table II. Appropriate equations were determined by visual inspection of the computer output plots for their linearity_ One such set of four curves for the plot of --In (1 -a) versus time is shown in Fig. 6. The

232 TABLE

II

KlNJZi-lC EQUATIONS I. 2. 3. 4. 5 6. 7_ 8_

USED IX THE COMPUTER

Poxer Iaw Contracting gwmetry 2D Diffusion controlled Erofav 3D DiKusion controlled Jandcr Prout-Thompkins Sazond order

n=$. 3, +, 1 and 2 1 -(I -z)~~~; n = 2 and 3 (I -z)In(I -2))tz [-In(1 -zjJ*:=; n=l,$,2,3and4 (1 -$z) - (I -&‘3 [I -(I -z)x’3]* lii[z[(i -a)] I --1 1-z In z 9;

9. Exponentid

TIME Fig. 6. Plots of -In(I

-2)

_4NALYSIS9

(SEC)

versus time for the dehydntions of aqueous mangancse(II) nitrate9.

choice of equation was then based on the exact degree of fit determined by the standard deviation arising from the calculation of k in the third stage of processing. This third stage consisted of the selection of the most likely kinetic equation or equations and the plotting of the best values of log k versus the reciprocal of the absoIute temperature, and a Ieast squares fit to determine the best straight line. The resulting activation energies, E, and the pre-exponential terms were printed out along with the piot II”, for use Vachuska and Voboril ” developed a program ca.lIed VACHVO on the GER computer, in which the first-order and also the second-order derivations of the time dependencies of both sampie weight and temperature are computed numerically with respect to time from experimental values of these quantities. A newer version of this program, denoted by the term VYRVACHVON”, in which a certain polynomic function is Iaid through the experimental points and its course is

233 determined by a least squares method. The computer then calculates the “corrected” input data from a given expressed function and using these data, numericaIIy differentiates. Both programs were written in the GIER-ALGOL language_ AIthough the programs or techniques were not discussed in detail, a digital computer was used to analyze the kinetics data obtained from TG by a number of investigatorsx5-19. One of these studies” used a Hewlett-Packard Model 91OOA programmable caIcuIator. Hughes and Hart” have deveIoped an anaIog simulation program, BASE, which was used for the prediction of a TG curve. The caIcuIation involved the plotting of the TG curve from the equation f(a) =

A ;

j-r

(8)

exp(j$)dt

where f(r) represents some description of the rate Iaw for the fractional decomposition (a) of the solid; A is the pre-exponential factor; a is the heating rate (d7/dt) and E the activation ener_q. In order to write a patch diagram for the program, they put y=exp(--E/lW)=e= where z = -E/RT

and dz = (E/RT’)dT.

(9) Then

dy = e’dz

(IO) dT = 2.4 e=

(11)

or j=2.4exp

(12)

is identica1 with Since the integral of j is y and because 2.4 exp (- EjRT)E/RT’ y, then it is assumed that E/RT’y, where y = exp (-E/NJ and generate f(y) (i.e., 2-4~ E/RT’), the integra1 of this function wiII be y. This process is represented by the patch diagram in Fig. 7. The computations were applied to the dehydration of I

Fig. 7. Patch diagram of Hughes and Hartz”.

234 HzO, a system which has been well studied by a number of investigators. Using the data given by Freeman and Carroll*, the caiculated and experimental curves are given in Fig. 8. It is interesting to note that the curve calculated by integrated methods using Akahira’s tables and the experimental parameters gave a curve which coincided niceIy with the computed one. CaC204-

---COMPUTED -EXPERIMENT 1 10

‘

SEC

TIME Fig. 8. Calcuiatcd and cqerimental TG cliwcs for CaCI04- HtOz3.

The in-house differences between results for duplicate samples tested by different laboratories under supposedly similar conditions Ied to interest in the effects of the rate and mode of heating, and also of fluctuations in temperature after heating, on the weight-Ioss curves. Because these problems did not lend themselves to direct soiution with the experimental equipment on hand, Gayle and Eggerz4 applied analog computation to study the_ importance of these variables. The caIculations were performed on an analog computer where the heating rate curves were programmed as the corresponding differential equations and the temperature integral of these used as input the Arrhenius equation. Integration of the latter provided the corresponding weight-Ioss curves_ The treatment provided an estimate of the infiuence of constant thermal errors and of fiuctuations about the programmed temperature level. It is noteworthy that symmetrical fiuctuations did not result in a can&.iation of errors

235 when the rate behavior was exponential rather than a linear function of temperature. The analog computer provided a graphic, reasonabIy accurate picture of the magnitude of such effects. DIFFERENTIALTHERMAL CALORMElRY

ANALYSIS

(DTA)

AND D IFFERENZTIAL SCANNING

(DSC)

Nearly all of the computer applications to DTA have been concerned with the calculations of reaction kinetics; they also provide the ideal means of simulating the DTA curve of a chemical reaction of known kinetics. One of the first of these applications was that by R& et al." in which the quantitative determination of kinetics by the methods of Borchardt and Daniels*” and Kissinger*’ were evaluated and compared. The DTA curve was generated numericahy by use of equations such as

where e is the activation ener,y and e:(d#/de,) the reaction order, @ is N/N0 (number of moles), c = rA (N,/v)“- ‘, and 0: is the dimensionless heating rate; in finitedifference form

where h represents the mesh spacing, A8,. A typicaI computer generated curve, in which the effect of actit-ation energy, e, on the DTA curve is plotted, is shown in i 1

y= 10’8 e;=0.0594

z

n=l E

I

o

14

16

i

/ I I

2

18

20

22

24

Fig_ 9. E&et of activation energy on DTA

26

mrve25.

28

30

32

236 Fig. 9_ Both the Iocation and the shape of thecurvesare affected, but thedependenceis inverse to that observed for the changes of the frequency factor. The fraction of sample decomposed (z) from DTA curves was calculated by an algorithm in ALGOL 60 language for a NCR Eiliot l&lode1 4130 computer by Skvara and Saravazs _ This algorithm calculated TXand log g(z) and plotted the latter a!; a function of temperature_ Comparison of the computed DTA data with the e:cperimental values for several dissociation reactions indicated a good agreement and applicability of the method. The use of a systems analog to improve the performance of a DTA apparatus and also to study the thermal effects in the DTA curve was investigated by Wilbum er &T9-30_ A finite-dillerence procedure was used to relate the thermal gradients within the samples and to generate or absorb heat according to a known equation. The influence of such physical properties on the shape and peak temperature of a ty-pica1 DTA curve ~3s c3lcul3ted on an ICT Model 1909 computerThe application of computer calculations to DTA studies of the crystallization kinetics of polymers was described by Gomicks4_ Calculations were made of the temperature of 3 poly-mcric sampIc durin g the cooling process using 3 Burroughs Model 5-X)0 computer. Marie er a1_55 used an IBM Model I 130 computer to prepare standard vapor pressure plots of In P versus 1,X, the vapor pressure data being obtained from DTA or DSC curves. The heat of vaporization was caIcuIated by the Haggenmacher method as modified by FishtineDavid ez ai_ 3 I used a digital temperature readout device in conjunction with an analog recorder for transition temperature measurement in DTA. No computations were made, howev-er, on the temperature measurements although temperature resolution was about 0.05”C at a heating rate of IO’C~min.

CT

:o

Trcnsier

cni’,

?!uzericc;: keyt?oarc! iieybocrc! multiplexer CTiS dis>icy CT ?el Digitci CT 15 Tamer c-r so Dizltcl vci’meter

CT

~~~

54

IO_ Mettlcr dstrr traraferspten connected to a Met&r

Dl-A 2000 system"=.

A

Tape punch

237 Amstutz’” described the MettIer data acquisition system which is capable of handling S-digir numbers of any format type or voItage level. A schematic diagram of the system is shown in Fig. 10. Expansion capabilities include digital and analog multiplexers, keyboards and switch banks for manual entry of data, timers, and programmers. Applications to DTA include off-line recording of raw data on punched paper tape or magnetic tape, and on-line processin g, ranging from simple peak area calculations by means of programmable desk-top calculators to the more complex numerical determinations of heat or reaction, kinetics, and purity analysis. One of the major applications of computers to differential scanning calorimetry (DSC) is in the determination of the purity of organic and inorganic compounds. The precision and accuracy of purity determinations by this technique have been reviewed by Joy et al. 33 _ One of the first programs for purity determinations using DSC data was that deveioped by DriscoII ef aL3’. Required input data are the sample mass and moiecuIar weight, instrument constants, a reference temperature at a point where rhe curve is stiI1 on the base Iine, and ordinate and abscissa measurements on the curve. One measurement shouId be at the meIting curve peak, but the intervals need not be of uniform size. A maximum of 99 pairs of readings can be accommodated by the program. The pro_mm divides the curve into 99 equal temperature intervals and integrates to obtain the AHf_ Temperature correction and baseline area correction are determined for each interval and the partial area is calculated. The program then applies successive one-half percent area corrections on each partial area and the total area and calculates the I/Fvalues. A least squares regression analysis is used in each corrected line until a minimum standard deviation of the poi es aboLt the caiculated line is reached. The i best vaIues” is then used in the subsequcn -nIcuIations. Output from the computer includes the AH,, T,, T,, moIe percent impurity, the l/F Iimits used, the percent correction applied, and the cryoscopic constant. A corrected mole percent impurity assuming solid solution behavior is also calculated_ The “linearization” of the T versus l_/Fcurve has been discussed35. Joy eC ai.33 rewrote the above program from Fortran into a basic program operable on a time-shared computer terminal. Other DSC purity determination programs have been developed by Barrall and DiIIer36 and Scott and Gray3’. Using an IBM Quiktran program, ElIerstein3s performed calculations of DSC curve data from the equation E

Alogl A Iog A,

=

2303R

CNJ!T)l I 12 [A log A,]

’

(1%

where I is the ordinate displacement between the base Iine and curve and A corresponds to the area remaining at temperature T. Plotting the left-hand side versus the bracketed expression gives a curve whose slope is E/2.303 R and the intercept will be equal to n, the order of reaction. Resuits from the Quiktran program are then fed into an IBF! Qltiktran common Iibrary program (FITLIN) which gives a “best” Iine fit of 2~ cAcuIated points.

238 Gray39 developed a program which accepts the DSC sample and baseline data, matches the “isothermal -, performs cumulative and total area integrations in units of caijg, corrects the temperature for thermal lag, and tabulates and plots ordinate v.*aIuesin specific heat units as well as cumulative area in enthalpy units. The analog data from the DSC instrument are digitized and transferred to paper tape with the use of the Perkin-Elmer ADS VI Analytical Data System for Thermal AnaIysis. The data are digitized every two seconds or every 0.133 degree. A computer plotter then plots the DSC curve and also the cumulative peak area in specific enthalpy units, cal/g_ Crosstey er aI.*’ used a computer reduction technique for the DSC isothermal curve which was developed to replace the use of a planimeter. The data reduction was divided into tu-o phases: (a) mechanism independent solufions for the reactant fraction, I, and various functions of z (where r is the reactant fraction remaining at time, t) and (6) solutions for mechanism dependent rate constants. For the rirstphase, the DATAR program was deveIoped which consisted of the following: Ordinal pcints, referred to as “coarse data”, and evenly spaced in time over the time span of the DSC curve, are read directIy into the computer_ Up to 1000 points may be read, but 40-50 are usuahy sufiicient for acceptable accuracy. The resultant fraction remaining at time, t, is caiculated by the equation

=(t) = l_?D)df_ ‘0

(16)

(0RD)dr _I r-z=, A Simpson’s RuIe procedure modified to handle odd numbers of intervals was used to calculate the inte_erls_ The pro_gramcalculates and prints the time in set and in min, z, in z, 1005 I,&, l/z’, (I--r)r, and log lOO[(I -zj/zc]. For the second stage, the PARACf pro-mm was used to determine the true rate constants, k, and k,. Other pro_gramswhich can be used to c&uIate reaction kinetics from DSC data are by Kauffman and F2eechJ’ and Rogers and SmithJ2_ Heuvel and Lind43 used a computer to correct DSC data for effects due to ‘thermal lag and heat capacity changes whiIe SondackC* dev-eloped a simple equation for linearization of data in DSC purity determinations.

Analysis of isoperibol czdorimetric data requires lengthy graphical procedures and/or tedious cafcuiations to obtain corrected resistance changes for the reaction and calibration experiments. The reaction experiment graphically resolves into two linear portions, the initial rating period (IRP), and the final rating period (FRP), connected by a curve for which no analytical equation is known. A program was developed for these calculations by Gayer and Baru~l~~. Friedman and co-workers4648 have developed a digital converter for recording

239 evolved gas analysis (EGA)-mass spectrometric (MS) data on punched paper tape. The data collection system is shown in Fig. 11. It is based on a very stable programmed power supply that steps the gate to preselected discrete ionic mass peak locations. In practice, analog gate voltages are determined for about 20 peak centers from m/e 1 to about 203, as monitored by a digitai voltmeter_ These are then analyzed signcl to se!ect

mie

Ii I

! I 1

temperature

i TEM-

I

REGULATOR

I

MASS chcr.ce

I ,

m/e

! SELECTOR

I f

VOLTMETER

s1g.na1

to

select next parameter

i

s:gncI

to

hold

i pcrcI!e! binary 1 code dlgitai data

f

I I

i CONVERTER

1

record

data

CLOCK

I

datz on perforated

Fig_ 11. Data colkction

system for EGA-MS

tape

after Friedman ex aL4’.

by a Ieast squares shared-time program using a polynomial equation thai includes five constants. If alI of the calculated points are within values equivalent to 10 13anosec of the observed time delay, the fit is accepted and a print-out is obtained for all analog gate voltages as a function of mass number, by interpolation and extrapointion. The punched paper tapes generated during a run are read by an optical reader and stored in a smali computer. A large computer then sorts the data by mass number and plots the data on a graphic plotter. The plotted data are corrected for background, instrument sensitivity, editorial corrections, and are normalized to I mg initial sample weight.

GibsonJg described a TG-MS system which contained a PDP 8jL computer interfaced to the mass spectrometer for on-line control of the mass spectral data_ A schematic diagram of the system is shown in Fig. 12_ The output analog signal from the mass spectrometer is integrated and converted to digital form by a 12-bit con-

Tape Q

Fig. 12. TG-MS

computer qstcm after Gibsonh9_

xrter and transfers it to magnetic tape. Two separate modes are possible: (1) data Iog&ng and (2) spectrum controi; they differ only in the manner in which they acquire data. Durin, 0 operation of the mass spectrometer, the pIotter gives a real-time gas reiease cxve, which is simply a pIot of the ion current from theelectron muItipiier at each recorded spectrum scanned. Other output routines include:

(1) (3) (3) (4) (5)

Reconstruction of a gas release pattern which normalizes the largest gas release peak or region to 100 and indeses the mass spectra during the run. Printed or pIotted spectra from any mass spectrum coIIected. PIots of individual mass (e_g_7 m:e = 18) peaks as a function of temperature_ Spectrum plots or printouts with positively identified mass scales and numeric ion intensities. Spectrum pIots or printouts with the background spectra subtracted to eliminate the effect of contaminants or backgrounds.

The TG and gas release curves of a sample of ApoIIo 15 riIIe soil is shown in Fig. 13. The individual m/e curves were automatically plotted. Kinetics caIcuIations on poIy(methyImethacrylate) using mass spectrometric thermal analysis (MTA) were described by Sakamoto et CZZ.‘~.Using the activation ener_q caIculated from the experimental data, the computer plots the logarithm of the reduced rate, dc/d0 versus the logarithm of the reduced time, 8. A comparison is then made between these curves which are calculated for various reaction mechanisms, and the curve which fits best is that of the first order reaction. In_~ham’* used samples pelletized into a specific geometry for convenience computer calculations of the kinetics resuits.

in

241

100

150 SPECTRUM

NO.

2t 3 4

1 100

I 300

I 500

Fig. 13. TG and gas release curves of Apollo

IS rille

I 1700

I 900

I 700

I 1300

OC

soil after Gibsonz9.

PfeiIsl discussed the application of digital computers to the statistical anaIysis of the TG measurements of edema. Computer graphics can also provide a useful and much-needed service in the thermal analysis of biological systems. It should be noted that computer data acquisition systems for thermal analysis instruments are available from the Perkin-Elmer Corporation3’, the DuPont 32 A data acqnisition system for a Company, and the Mettler Instrument Company . thermal anaIyzer has also been described by Yui et al. ’ 2_ ACKNOWLEDGMENT

The support of this work by the Robert Texas, is gratefully acknowledged.

A. Welch

Foundation

of Houston,

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